Not sure I can help, but looks like you needed a response. I've found this map,(http://www.dohamap.info/map/) which should be useful in deciding what areas would be most handy for your commute.

Airport is bottom right. You can zoom in etc, and sort by district. I've found it useful trying to sort out my own place to live! I've not moved out yet, but fly out on the 2nd of Feb, but the one thing I've heard, and saw when I was over, is that traffic is mental! So I would suggest if you want to spend time with your kids, then you either live close to work, or close to their school or nursery. There appears to be lots of Compounds out towards the airport, so you shouldn't have too much trouble. Hope this helps a little.